So where exactly did he put that Goya?

Some people can’t stand Danny Boyle’s approach to filmmaking. All that hyperactive cutting and color-saturated imagery, the in-your-face camera angles yoked to tempos fueled by breakneck music — at times Boyle can seem more like a DJ than a director. But because his style is generally wedded to strong story lines — in movies like “Slumdog Millionaire,” “127 Hours,” “28 Days Later,” and “Trainspotting” — a lot of audiences, critics, and Oscar voters follow him willingly.

With “Trance,” story becomes just another element in Boyle’s commercial pop-Cubism, and the results are nearly fatal. The title couldn’t be more misleading, since the movie’s the opposite of dozy and quiescent — it’s what you might get if a post-doctoral student put a heist movie in a Cuisinart. James McAvoy plays our narrator Simon, a London auction-house employee who gets conked on the head during a brazen mid-bid robbery by a gang of thieves. He wakes up in the hospital minus a chunk of his memory. Simon remembers that he was in on the job, but he can’t remember where he put the booty: Goya’s spectral 1798 painting “Witches in the Air.”

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Unfortunately for him, the gang’s leader, Franck, is played by Vincent Cassell (”Irreversible,” “Ocean’s Twelve”), who most audiences understand by now is capable of anything in the interests of persuasion, starting with fingernail removal and proceeding from there. If Franck could rip the memory from Simon’s battered brain, he would. But he can’t. So he hires a hypnotherapist.

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Her name is Elizabeth, and she’s played by Rosario Dawson with a professionalism that becomes increasingly shredded over the course of the plot. I confess it: The presence of Dawson in any movie tends to dismantle this reviewer’s critical faculties, so it’s a mark of how spectacularly bonkers “Trance” gets that that I feel like I deserve a long vacation from her and everyone else involved.

The gangster wants Simon to wear a wire in his sessions, the faster to get the goods, but Elizabeth tumbles to the trick and agrees to continue only if she’ll get a cut. (Trust me, I haven’t spoiled a tenth of what the movie has up its overstuffed sleeve.) “Trance” turns into a feverish three-handed poker game of greed and desire, with Simon and Franck crushing on Elizabeth, Elizabeth throwing down new cards, and everyone bluffing everyone else. The other gang members are there for local color and the occasional bullet in the crotch.

The trick with tricky movies lies in keeping the audience on a tightrope of pleasure and belief, faking us out with each new reveal while talking us into renewing our trust again and again. If we get to the end and feel both exhausted and played fair by, all’s well. “Trance,” by contrast, piles on one surprise after another, until it goes far past fair and close to Dada. Coincidences and connections are introduced until it’s clear the filmmakers are interested only in what they can get away with. Our allegiances are bounced back and forth like badminton birdies. We learn more about Elizabeth’s personal grooming habits than you’d expect from a mainstream film.

All of this gamesmanship can be great fun when done in the right spirit, and Boyle is nothing if not a spirited director. “Trance” is lunatic but undeniably entertaining for much of its running time. At a certain point, though — say, after the third or fourth narrative switchback — our emotional involvement is down to nil. Only the cheerfully sadistic Franck has any sympathy by the end. He may be a psychopath, but at least he’s reasonable.

The movie’s baroque, diamond-hard, and beautiful to look at, shot to a gleaming fare-thee-well by Boyle’s usual coconspirator Anthony Dod Mantle. “Trance” is mesmerizing nonsense, but it is, in the end, nonsense: a succession of fake-outs that leaves an audience feeling merely burned. It’s one thing to employ an unreliable narrator. Boyle’s in danger of becoming an unreliable filmmaker.